feat(ui): Interactive chip for tasks with an open ConPTY session

A task driven by hand in Mission Control is Idle with an Active worktree, so its
lifecycle chip read "Parked" — indistinguishable from a task genuinely set aside.
The shell now mirrors Mission Control's open panes onto the rows, which show an
accent "Interactive" chip instead; tapping it surfaces Mission Control and
focuses that pane (the open command already dedupes by task id).

src/ClaudeDo.Ui/ViewModels/Islands/TasksIslandViewModel.cs

@@ -21,6 +21,9 @@ public sealed partial class TasksIslandViewModel : ViewModelBase, IDisposable
     private readonly Dictionary<string, bool> _expandedState = new();
     private ListNavItemViewModel? _currentList;
     private CancellationTokenSource? _loadCts;
+    // Task ids with a live ConPTY pane in Mission Control; kept here so rows loaded later still
+    // pick the flag up (see SyncInteractiveSessions).
+    private readonly HashSet<string> _interactiveSessionIds = new();
     private static readonly TaskListFilterRegistry _filters = new();
 
     public event EventHandler? SelectionChanged;
@@ -274,6 +277,7 @@ public sealed partial class TasksIslandViewModel : ViewModelBase, IDisposable
             {
                 var row = TaskRowViewModel.FromEntity(t);
                 row.ShowListChip = showListChip;
+                row.HasInteractiveSession = _interactiveSessionIds.Contains(row.Id);
                 Items.Add(row);
             }
 
@@ -441,6 +445,17 @@ public sealed partial class TasksIslandViewModel : ViewModelBase, IDisposable
         TasksChanged?.Invoke(this, EventArgs.Empty);
     }
 
+    /// <summary>Replaces the set of tasks that currently have an open interactive (ConPTY) session,
+    /// so their lifecycle chip reads "Interactive" instead of "Parked".</summary>
+    public void SyncInteractiveSessions(IEnumerable<string> taskIds)
+    {
+        _interactiveSessionIds.Clear();
+        foreach (var id in taskIds)
+            _interactiveSessionIds.Add(id);
+        foreach (var r in Items)
+            r.HasInteractiveSession = _interactiveSessionIds.Contains(r.Id);
+    }
+
     public bool CanReorder => _currentList?.Kind == ListKind.User;
 
     public void ClearDropHints()